Prediction of surface topography due to finite pixel spacing in FIB milling of rectangular boxes and trenches

Abstract

For applying focused ion beam technologies in fabrication of the predetermined structures it is essential to evaluate the ion dose delivered to the specimen by the beam and on this basis to predict the formed topography. In this article the authors obtain exact expressions for the ion dose distribution arising in the irradiated region when trenches and rectangular boxes are milled. Based on them the authors describe the surface shape of the structures under consideration when the constant sputtering yield conditions are realized during the milling process. The rather cumbersome analytical description can be transformed into the simple form for milled regions at the distance slightly exceeding the beam diameter from the structure boundaries. Within this region the milled surface shape can be represented as a sum of sinusoidal functions analogous to one- or two-dimensional Fourier series. For typical structure fabrication when the distance between neighboring beam stops is less than approximately two beam diameters the authors derive simple formulas for evaluating the mean depth and the peak-to-valley surface roughness. The authors also estimate when constant sputtering yield conditions can be utilized for the description of the actual milling process. To testify the theoretical considerations two trenches and four rectangular boxes were prepared. In addition, several deep and shallow dotlike structures were created for evaluating the ion flux density determining the beam shape, which was presented as the sum of two Gaussian functions. Peripheral regions of the deep dots cross-sections allow us to find the standard deviation of the second Gaussian function while the standard deviation of the first Gaussian function and the weight factor are retrieved using the milling profiles of the shallow dots. A set of parameters describing the ion flux density of the beam and milling process enables calculating the surface shapes and cross-sectional profiles of the fabricated structures. The authors show that the simulated shapes of the trench and the box and scanning electron microscope images of these structures are similar in appearance. Comparison of experiment and theoretical milling profiles demonstrates good agreement between them. Theoretically estimated mean depth and peak-to-valley surface roughness are consistent with experimental data.